nature of magnetic ordering in cobalt based spinels

Faculty Scholarship

2017

Nature of Magnetic Ordering in Cobalt‐Based Spinels Nature of Magnetic Ordering in Cobalt Based Spinels

Subhash Thota Indian Institute of Technology

Sobhit Singh West Virginia University

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Chapter 4

Nature of Magnetic Ordering in Cobalt‐Based Spinels

Subhash Thota and Sobhit Singh

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65913

Provisional chapter

Nature of Magnetic Ordering in Cobalt‐Based Spinels

Subhash Thota and Sobhit Singh

Additional information is available at the end of the chapter

Abstract

In this chapter, the nature of magnetic ordering in cobalt‐based spinels Co3O4,Co2SnO4, Co2TiO4, and Co2MnO4 is reviewed, and some new results that have notbeen reported before are presented. A systematic comparative analysis of variousresults available in the literature is presented with a focus on how occupation of thedifferent cations on the A‐ and B‐sites and their electronic states affect the magneticproperties. This chapter specifically focuses on the issues related to (i) surface andfinite‐size effects in pure Co3O4, (ii) magnetic‐compensation effect, (iii) co‐existence offerrimagnetism and spin‐glass‐like ordering, (iv) giant coercivity (HC) and exchangebias (HEB) below the glassy state, and (v) sign‐reversal behavior of HEB across the ferri/antiferromagnetic Néel temperature (TN) in Co2TiO4 and Co2SnO4. Finally, someresults on the low‐temperature anomalous magnetic behavior of Co2MnO4 spinels arepresented.

Keywords: ferrimagnetic materials, Néel temperature, spin‐glass, exchange bias

1. Introduction

The atomic arrangement of the spinel compounds is interpreted as a pseudo‐close‐packedarrangement of the oxygen anions with divalent cations occupying tetrahedral A‐sites andtrivalent cations residing at the octahedral B‐sites of the cubic unit cell of space groupFd‐3m(227). A spinel with the configuration (A2+) [B2

3+] O4 is termed as “normal spinel”whereas the other possible configuration (B3+) [A2+B3+] O4 is called “inverse spinel.” Thecontinuum of possible atomic distribution between these two extremes is quantified by aparameter denoted as x (inversion parameter), which describes the fraction of “B” cations ontetrahedral sites. Thus, x = 0 for a normal spinel, 2/3 for a spinel with entirely arbitraryconfiguration, and 1 for a fully inverse spinel. Among many varieties of spinel compounds,

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,and reproduction in any medium, provided the original work is properly cited.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited.

ferrites and cobaltites are widely used in the high‐frequency electronic circuit componentssuch as transformers, noise filters, and magnetic recording heads [1, 2]. The key property ofthese spinels is that at high frequencies (>1 MHz), their dielectric permittivity (ε) and magneticpermeability (μ) are much higher than those of metals with low loss‐factor (tanδ). Theseproperties make them very advantageous for the development of magnetic components usedin the power electronics industry. Also, the nanostructures of these spinels continue to receivelarge attention because of their potential applications in solid‐oxide fuel cells, Li‐ion batteries,thermistors, magnetic recording, microwave, and RF devices [1, 2].

In this review, we mainly focus on the nature of magnetic ordering of several insulating cobaltspinels of type Co2MO4 (where “M” is the tetravalent or trivalent metal cation such as Sn, Ti,Mn, Si, etc.) which are not yet well studied in literature. This review will primarily illustratehow the magnetic ordering changes when we substitute the above‐listed metal cations at thetetrahedral B‐sites. It is well known that the dilution of magnetic elements significantlydisrupts the long‐range magnetic ordering and leads to more exotic properties like magneticfrustration, polarity reversal exchange bias, and reentrant spin‐glass state near the magnetic‐phase transition [3, 4]. The dilution essentially alters the super‐exchange interactions of JAB, JBB,and JAA between the magnetic ions, which is the main source of anomalous magnetic behavior.In this review, we first start with the simplest case of antiferromagnetic (AFM) normal‐spinelCo3O4 with configuration (Co2+)[Co2

3+]O4 and discuss the role of surface and finite‐size effectson antiferromagnetic (AFM) ordering. In the second section, we focus on the coexistence offerrimagnetism and low‐temperature spin‐glass behavior of cobalt orthostannate (Co2SnO4)and cobalt orthotitanate (Co2TiO4). A detailed comparative analysis of some recent experi‐mental results dealing with the temperature and frequency dependence of ac‐magneticsusceptibility is presented. In the subsequent section, some unusual magnetic properties ofCo2MnO4 are discussed.

2. Magnetic properties of bulk versus nanocrystalline Co3O4

Cobalt forms two binary compounds with oxygen: CoO and Co3O4. While CoO has face‐centered cubic (NaCl‐type) structure, Co3O4 shows a normal‐spinel structure with a cubic closepacked arrangement of oxygen ions and Co2+ and Co3+ ions occupying the tetrahedral “8a” andthe octahedral “16d” sites, respectively [5]. The magnetic properties of Co3O4 were firstinvestigated over 58 years ago; however, its magnetic behavior under reduced dimensions stillattracted immense scientific interest mainly because of its distinctly different magneticordering under nanoscale as compared to its bulk counterpart [6]. Co3O4 can be synthesizedin various nanostructural forms such as nanorods, nanosheets, and ordered nanoflowers withultrafine porosity [7–10]. Such engineered nanostructures play vital roles as catalysts, gassensors, magneto‐electronics, electrochromic devices, and high‐temperature solar selectiveabsorbers [11–18]. At first glance, the normal‐spinel structure of Co3O4 may look similar to thatof Fe3O4 (inverse spinel) but Co3O4 exhibits strikingly different magnetic ordering ascompared to Fe3O4. In particular, Co3O4 does not exhibit ferrimagnetic ordering of the typeobserved in Fe3O4 because Co3+ ions on the octahedral B‐sites are in the low spin S = 0 state [5].

Magnetic Spinels- Synthesis, Properties and Applications76

Instead, it exhibits antiferromagnetic ordering with each Co2+ ion at the A‐site having fourneighboring Co2+ ions of opposite spins (with an effective magnetic moment of μeff ∼ 4.14 μB)[5]. Earlier studies by Roth reported that below the Néel temperature TN ∼ 40 K, Co3O4 becomesantiferromagnetic in which the uncorrelated spins of the 8Co2+ (in 8(a), F.C. +000, 14 14 14 ) cationsin the paramagnetic state (space group O7

h—Fd‐3m) are split in the antiferromagnetic state(space group T2

d—F43m) into the two sublattices with oppositely directed spins of 4Co2+ ↑ (4(a),+000) and 4Co2+ ↓ (4(c) 14 14 14 ) [5–7]. For T < TN, the neutron diffraction studies did not show anyevidence of a structural phase transition.

As shown in Figure 1, the recent magnetic studies by Dutta et al. [6] have reported a significantdifference in the antiferromagnetic ordering temperature TN ∼ 30 K of Co3O4 as compared tothe earlier data (40 K); this new result however is in excellent agreement with TN = 29.92 ± 0.03K obtained by the heat capacity Cp versus T measurements reported by Khriplovich et al. [19].It is well known that the peak in the magnetic susceptibility data of antiferromagnets usuallyoccurs at a temperature few percent higher than TN because the magnetic specific heat of asimple antiferromagnet (in particular, the singular behavior in the region of the transition)should be closely similar to the behavior of the function d(χpT)/dT [14]. Therefore, TN is better

Figure 1. (a) Temperature dependence of the dc‐magnetic susceptibility χ(T) for bulk Co3O4 under the zero‐field‐cooled(ZFC) and field‐cooled (FC) conditions. Here, Tp denotes the peak position in χ versus T plots. (b) Plots of (χpT) versusT (LHS scale) and d(χpT)/dT versus T plots (RHS scale) for the bulk Co3O4. Here, the paramagnetic susceptibility χp =χ–χ0 with χ0 = 3.06 × 10‐6 emu/g Oe being the temperature‐independent contribution [6, 7].

Nature of Magnetic Ordering in Cobalt‐Based Spinelshttp://dx.doi.org/10.5772/65913

77

defined by the peak in ∂(χT)/∂T versus T plot [20]. Figure 1 shows the temperature dependenceof paramagnetic susceptibility χp(T) (LHS scale) and d(χpT)/dT versus T (RHS scale). For bulkCo3O4 the peak temperature value (30 K) in the d(χpT)/dT versus T plots is lower than TN ≃ 40K often quoted for Co3O4 [5–7, 9–10]. Thus, TN = 30 K determined from two independenttechniques (i.e., χp and Cp measurements) is consistent with each other and is the accuratecharacteristic value for bulk Co3O4. On the other hand, the nanoparticles of Co3O4 exhibit lowerTN values and reduced magnetic moment than the bulk value (30 K, 4.14 μB) which is aconsequence of finite‐size and surface effects [6]. Salabas et al. first reported Co3O4 nanowiresof diameter 8 nm and lengths of up to 100 nm by the nanocasting route and observed TB ≃ 30K and exchange bias (He) for T < TB [10].

Figure 2. Variation of the Néel temperature TN of Co3O4 as a function of particle size (d). The data pertaining to solid‐square symbols are taken from Refs. [6–8] in which TN is considered as a peak point in”d(χpT)/dT” versus”T” data.However, the data related to solid green circles are taken from Refs. [8, 9] in which TN is considered as just the peakpoint in the “χ“versus”T” plot, not from the derivative plots. The scattered symbols are the raw data corresponding toTN and the solid lines are the best fit to Eq. (1).

A plot of TN values versus particle size d reported by several authors for various crystallitesizes of Co3O4 is shown in Figure 2. The lowest TN value reported till now is about 15 ± 2 K for4.34 nm size Co3O4 particles [8]. These nanoparticles were synthesized using biologicalcontainers of Listeria innocua Dps proteins and LDps as constraining vessels. Lin and Chenstudied the magnetic properties of various sizes (diameter d = 16, 35, and 75 nm) of Co3O4

nanoparticles prepared by chemical methods using CoSO4 and CoCl2 as precursors [9]. Theseauthors reported that the variation of TN follows the finite‐size scaling relation:


( ) ( ) 0N NT D T 1

d

lxé ùæ ö= ¥ -ê úç ÷è øê úë û

(1)

for various sizes of Co3O4 nanoparticles. Accordingly, they obtained the shift exponent � = 1.1± 0.2 and the correlation length ξo = 2.8 ± 0.3 nm from the fitting analysis of TN versus d(Figure 2). However, these authors considered TN values as the direct peak temperature valuesfrom χ versus T instead of the peak point in d(χpT)/dT. Also, for the bulk grain sizes TN (∞) =40 K was considered instead of 30 K obtained from d(χpT)/dT analysis as discussed above.Therefore, we repeated the analysis but considering TN values obtained from d(χpT)/dT versusT and the TN (∞) = 30 K for various sizes of the Co3O4 nanoparticles obtained by sol‐gel process(these values were obtained from our earlier works [6, 7]). Accordingly, we obtained � = 1.201± 0.2 and the correlation length ξo = 2.423 ± 0.46 nm, which are slightly different from the earlierreported values � = 1.1 ± 0.2 and the correlation length ξo = 2.8 ± 0.3 nm [9]. Nonetheless, inboth the cases TN follows the finite‐size scaling relation Eq. (1).

For T > TN, the data of χ versus T (Figure 3) are fitted to the modified Curie‐Weiss law χP = χ0

+ [C/(T + θ)] with C = Nμ2/3kB, μ2 = g2 J(J + 1)μB2, θ is the Curie‐Weiss temperature and χ0 contains

two contributions: the temperature‐independent orbital contribution mentioned earlier and

Figure 3. 1/χp versus T plots for the bulk and nanocrystalline (∼17 nm) Co3O4 with χ0 = 3.06 × 10‐6 emu/g Oe (LHSscale). The solid lines represent linear fit to the Curie‐Weiss law: χp = C/(T + θ). On the RHS scale same figures areplotted except for χ0 = 9 × 10‐6 and 7.5 × 10‐6 emu/g Oe for the bulk and Co3O4 nanoparticles of size ∼17 nm, respectively[6, 7].


79

the diamagnetic component χd = −3.3 × 10−7 emu/g Oe [6]. Usually χ0 is estimated from the plotof χ versus 1/T in the limit of 1/T → 0 using the high‐temperature data. The value of χ0 wasestimated as 3.06 × 10−6 emu/g Oe for bulk Co3O4 using the inverse paramagnetic susceptibility(1/χP) versus temperature (T) data (shown in the left‐hand‐side scale of Figure 3) [5, 6]. Asimilar procedure for experimental data, shown in the right‐hand side scale of Figure 3, yieldsχ0 = 9 × 10−6 and 7.5 × 10−6 emu/g Oe for the bulk and nanoparticles (size ∼17 nm) of Co3O4,respectively.

It is well known that the origin of the antiferromagnetic ordering in transition metal oxidescan be explained by the super‐exchange interaction between the magnetic elements via oxygenion. In the present case, there are two possible paths for super‐exchange interaction betweenmagnetic ions in Co3O4, i.e., Co2+ ions: (tetrahedral site) A – O (oxygen) – A (tetrahedral site)and A – O – B – O – A with the number of nearest‐neighbors z1 = 4 and next‐nearest‐neighborsz2 = 12, respectively. If the corresponding exchange constants are represented by J1ex and J2ex,the expressions for TN and θ, using the molecular‐field theory, can be written as [5, 6]

( )N 1 1 2 2( 1)T3 ex ex

B

J J J z J zk+

= - (2)

( )1 1 2 2( 1)3 ex ex

B

J J J z J zk

q += + (3)

In order to determine J1ex and J2ex, the magnitude of effective J(J + 1) for Co2+ is required. Sincethe Curie constant C is equivalent to Nμ2/3kB with μ = g [ J(J + 1)]½μB where g is the Landé g‐factor and J is the total angular momentum. Using the magnitude of g = 2 and C from Fig‐ure 3, one can estimate the effective magnetic moment μeff = 4.27μB for bulk Co3O4 and μ =4.09μB for Co3O4 nanoparticles of size ∼17 nm. The spin contribution to the above magnitudesof μ is 3.87μB for Co2+ with spin S = 3/2. Obviously, there is some additional contributionresulting from the partially restored orbital angular moment for the 4F9/2 ground state ofCo2+ [5, 6]. Using Eqs. (2) and (3) and the values of “θ,” “TN,” and “μ” for the two cases yieldsJ 1ex = 11.7 and J2ex = 2.3 K for bulk, and J1ex = 11.5 and J2ex = 2.3 K for the Co3O4 nanoparticles (d∼ 17 nm). Thus, both the exchange constants J 1ex and J2ex correspond to antiferromagneticcoupling. From the magnitudes of C in Figure 3, the value of μ is obtained as 3.28 and 3.43 μB

for bulk and Co3O4 nanoparticles (d ∼17 nm), respectively. These magnitudes of μ are lowerthan the spin contribution (3.87 μB) of Co2+ ion itself. Consequently, the magnitudes of “θ” inFigure 3 seem to be questionable. This may be due to the fact that the use of molecular‐fieldtheory in determining the exchange constants has its own limitations since higher order spincorrelations are neglected in this model [6].

For a typical bulk antiferromagnet, below TN, the magnetization is expected to vary linearlywith applied external magnetic field H below the spin‐flop field. Therefore, the correspondingcoercive field Hc and exchange‐bias field He must become zero. This was indeed observed inbulk Co3O4 (Figure 4a) [5, 6]. Conversely, for the Co3O4 nanoparticles (d ∼ 17 nm), the data at


5 K show a symmetric hysteresis loop with Hc = 200 Oe for the zero‐field‐cooled sample andasymmetric (shifted) hysteresis loop with Hc = 250 Oe and He = −350 Oe for the sample cooledin magnetic field H = 20 kOe from 300 to 5 K as shown in Figure 4b. Thus, cooling the samplein a magnetic field produces an exchange bias and leads to the enhancement of Hc as well. Thetemperature dependence of Hc and He for the nanoparticles of Co3O4 cooled under H = 20 kOefrom 300 K to the measuring temperature is shown in Figure 5. Both Hc and He approach tozero above TN. The inset of Figure 5 depicts the training effect, i.e., change in the magnitudeof He for the sample cycled through several successive hysteresis loops (designated by “n” at5 K) [6, 10]. A similar effect has been recently reported by Salabas et al. [10] in the Co3O4

nanowires of 8 nm diameter although the magnitudes of He and Hc in their case are somewhatsmaller. The existence of the exchange bias suggests the presence of a ferromagnetic (shell)/antiferromagnetic (core) interface with FM‐like surface spins covering the core of the antifer‐romagnetically ordered spins in the nanoparticles of Co3O4. Salabas et al. reported that He fallsby ~25% measured between the first and the second loops. The observation of the trainingeffect and open loops of up to 55 kOe suggests that the surface spins are in an unstable spin‐glass‐like state [10]. Such a spin‐glass ordering results from the weaker exchange couplingexperienced by the surface spins due to reduced coordination at the surface. These effectshowever disappear above TN when the spins in the core become disordered. The observation

Figure 4. The magnetization (M) versus external applied field (H) plots recorded in standard five‐cycle hysteresis modefor bulk and nanoparticles (d ∼17 nm) of Co3O4 measured at 5 K in the lower field region of ±1 kOe. (a) Irreversibilityobserved for the direct and reverse field scans for bulk Co3O4, however, (b) a asymmetric shift in the hysteresis loopwith enhanced coercivity can be clearly noticed in the case of nanoparticles (d ∼ 17 nm) of Co3O4 measured underfield‐cooled protocol (FC) of H = 20 kOe [6, 7].


81

of somewhat lower magnetic moment per Co2+ ion, smaller values of exchange constants J1ex

and J2ex, and lower TN was noticed for the nanoparticles of Co3O4 in relation to the bulk Co3O4.This could be due to the weak exchange coupling and reduced coordination of the surfacespins.

Figure 5. The temperature dependence of Hc and He for the nanoparticles of Co3O4 (d ∼ 17nm) measured from T = 5 to40 K under field‐cooled (FC) mode at 20 kOe and at 5 K under zero‐field‐cooled (ZFC) condition [6]. One can clearlynotice Hc → 0, He → 0 as T approaches TN. The inset shows progressive decrease of the magnitude of He after succes‐sive scan (number of cycles”n”) at 5 K [6].

3. Co‐existence of ferrimagnetism and spin‐glass states in some invertedspinels

In 1975, Sherrington and Kirkpatrick (SK) first predicted the reentrant behavior of spinels usingmean‐field approach for certain relative values of the temperature and exchange interaction[21, 22]. Later, Gabay and Toulouse extended the SK Ising model calculation to the vector spinglasses and showed that it is possible to have multiple phase transitions such as ferro/ferri/

antiferromagnetic state paramagnetic state Mixed phase‐1 Mixed phase‐2 [22,23]. The present section deals with such kind of systems in which the longitudinal ferrimag‐netic ordering coexists with the transverse spin‐glass state below the Néel temperature TN [23–28]. In this connection, we mainly focus on the magnetic ordering in two inverse‐spinelsystems, namely (i) cobalt orthostannate (Co2SnO4) and (ii) cobalt orthotitanate (Co2TiO4)which exhibits the reentrant spin‐glass behavior [24–40]. At first glimpse, both systemsCo2SnO4 and Co2TiO4 are expected to show similar magnetic properties because of the fact that


nonmagnetic ions Sn and Ti play identical role on the global magnetic ordering of the system.But in reality, they exhibit markedly different magnetic structures below their ferrimagneticNéel temperatures [24–40], which is discussed in detail below.

Usually, the ferrimagnetic ordering in Co2SnO4 and Co2TiO4 arises from the unequal magneticmoments of Co2+ ions at the tetrahedral A‐sites and octahedral B‐sites [24–40]. The corre‐sponding magnetic moment at the tetrahedral A‐sites μ(A) is equal to 3.87 μB and the magneticmoment at octahedral B‐sites μ(B) is equal to 5.19 and 4.91 μB for Co2TiO4 and Co2SnO4,respectively [27–33]. In 1976, Harmon et al. first reported the low‐temperature magneticproperties of polycrystalline Co2SnO4 system and showed the evidence for ferrimagneticordering with TN ∼ 44 ± 2 K [24]. They also suggested that Co2SnO4 should contain two equallypopulated sublattices that align collinearly and couple antiferromagnetically [24]. On the basisof the Mössbauer spectroscopy results, these authors calculated the internal dipolar fields atthe Sn sites from the two Co2+ sublattices to be > 80 kOe [24]. They also reported very highvalues of coercive field HC > 50 kOe below TN [24]. The reported magnetization value at 16 Kper Co2+ ion was about 2.2 × 10−3 μB with zero magnetization value at 12 K. The Curie‐Weissconstant (C) = 4.3 ± 0.2 emu/mol, and the effective magnetic moment of the Co2+ ions = 5.0 ± 0.2 μB was close to the standard value of 4.13 emu/mol and 4.8 μB, respectively. A year later,Sagredo et al. reported that the zero‐field‐cooled and field‐cooled magnetization curves ofsingle crystal Co2SnO4 exhibit strong irreversibility below TN [39].

Sagredo et al. reported that thermoremanent magnetization, magnetic training effects, andspin‐glass phases present in this system are driven by the disordered‐spin configurations [39].Accordingly, they speculated that the random distribution of Sn4+ ions on the B‐sites mightbreak the octahedral symmetry of the crystal field and result in the frustrated magneticbehavior [39]. In 1987, Srivastava et al. reported multiple peaks in the temperature dependenceof ac‐magnetic susceptibility χac(T) for both Co2SnO4 and Co2TiO4 below their TN providingthe evidence of Gabay and Tolouse mixed‐phase transitions [25, 28]. Nevertheless, some recentstudies proved the existence of transverse spin‐glass state TSG (∼39 K) just below the TN (= 41K) in Co2SnO4 [27, 38, 40]. Similar type of results in Co2TiO4 was reported by Hubsch et al. andSrivastava et al. but with different TSG (∼46 K) and TN (=55 K) [25, 28, 31, 34].

In order to get a precise understanding of the magnetic properties of these systems, we haveplotted the temperature dependence of dc‐magnetic susceptibility χdc(T) for both Co2SnO4 andCo2TiO4 measured under ZFC and FC (H@100 Oe) conditions in Figure 6. These χdc(T) plotsshow typical characteristics of ferrimagnetic ordering with peaks across the Néel temperaturesTN = 47 K (for Co2TiO4) and 39 K (for Co2SnO4). However, for T ≤ 31.7 K an opposite trend inthe χdc(T) values was noticed for Co2TiO4 with χdc ∼ 0 at magnetic‐compensation temperatureTCMP = 31.7 K at which the two‐bulk sublattices magnetizations completely balances with eachother [31–33]. Such compensation behavior in Co2SnO4 system is expected to appear at verylow temperatures (T < 10 K) as χdc(T) approaches to zero. Consequently, χdc‐ZFC exhibits negativemagnetization until TSG. It is expected that the different magnetic moments on the tetrahedral(A) and the octahedral (B) sites, and their different temperature dependence (i.e., μA(T), μB(T))play a major role on the global magnetic ordering of both systems.


83

Figure 6. The temperature dependence of dc‐magnetic susceptibility χdc(T) measured under ZFC and FC (H@100 Oe)conditions for both Co2TiO4 (LHS) and Co2SnO4 (RHS). The dotted line shows the TCMP.

Recent X‐ray photoelectron spectroscopic studies reveal that the crystal structure of Co2TiO4

consists of some fraction of trivalent cobalt and titanium ions at the octahedral sites, i.e.,[Co2+][Co3+Ti3+]O4 instead of [Co2+][Co2+Ti4+]O4 [34]. On the contrary, the Co2SnO4 shows theperfect tetravalent nature of stannous ions without any trivalent signatures of Co3+ [Co2+][Co2+Sn4+]O4 [27]. Such distinctly different electronic structure of the ions on the B‐sites of cobaltorthotitanate plays a significant role on the anomalous magnetic ordering below TN, forexample, exhibiting the magnetic‐compensation behavior, sign reversible zero‐field exchange‐bias, and negative slopes in the Arrott plots (H/M versus M2) [27, 34].

At high temperatures (for all T > TN), the experimental data of inverse dc‐magnetic suscepti‐bility (χ−1) for both the systems Co2TiO4 and Co2SnO4 fit well with the modified Néel expressionfor ferrimagnets (1/χ) = (T/C) + (1/χ 0) – [σ0/(T − θ)]. Table 1 summarizes various fittingparameters obtained from the Néel expression for both Co2SnO4 and Co2TiO4. The fit forCo2TiO4 yields the following parameters: χ0 = 41.92 × 10−3 emu/mol‐Oe, σ0 = 31.55 mol‐Oe‐K/emu, C = 5.245 emu K/mol Oe, θ = 49.85 K. The ratio C/χ0 = Ta =125.1 K represents the strengthof the antiferromagnetic exchange coupling between the spins on the A‐ and B‐sites and isoften termed as the asymptotic Curie temperature Ta. For both the systems, the effectivemagnetic moment μeff is determined from the formula C = Nμeff

2/3kB. The experimentallyobserved magnetic moments at the B‐sites μ(B) = 5.19 μB obtained from the temperaturedependence of magnetization values are in line with the above‐discussed spectroscopicproperties of Co2TiO4, i.e., the total moment μ(B) is perfectly matching with the contribution

from the magnetic moments due to Co3+ (4.89 μB) and Ti3+ (1.73 μB), μ(B) = �Co+3 2+ �Ti+3 2[34]. Also, the analysis of the dc and ac susceptibilities combined with the weak anomaliesobserved in the Cp versus T data has shown the existence of a quasi‐long‐range ferrimagneticstate below TN ~ 47.8 K and a compensation temperature of TCMP ~ 32 K [34].


System C (emu K/mol/Oe) χo (emu/mol/Oe) σo (Oe mol K emu−1) θ (K) μeff (μB) μ (A) (μB) μ(B) (μB)

Co2TiO4 5.245 0.0419 31.55 49.85 6.5 3.87 5.19

NAA NAB NBB JAA JAB JBB

17.319 35.700 12.720 3.25 kB 4.47 kB 3.18 kB

Co2SnO4 4.889 0.0436 102.370 39.5 6.25 3.87 4.91

NAA NAB NBB JAA JAB JBB

21.564 33.201 10.68 4.05 kB 5.26 kB 4.28 kB

Table 1. The list of various parameters obtained from the Néel fit of χ−1 versus T curve recorded under zero‐field‐cooled condition.

The real and imaginary components of the temperature dependence of ac‐susceptibility dataχac(T) (= χ′(T) + i χ″(T)) recorded at different frequencies for both the polycrystalline samplesCo2SnO4 and Co2TiO4 show the dispersion in their peak positions (TP(f)) similar to the com‐pounds exhibiting spin‐glass‐like ordering [27, 33]. Figure 8 shows the χ′(T) and χ″(T) dataof Co2SnO4 and Co2TiO4 recorded at different measuring frequencies ranging from 0.17 to 1202Hz with peak‐to‐peak field amplitude Hac = 4 Oe under zero dc‐bias field. It is clear from thesefigures that the peaks seen in both cases show pronounced frequency dependence, whichsuggests the dynamical features analogous to that of observed in spin‐glass systems. A detailedanalysis of such frequency dependence of χ′(T) and χ″(T) using two scaling laws describedbelow provides the evidence for spin‐glass‐like characteristics below TN. For example,applying the Vogel‐Fulcher law (below equation) for interacting particles

( )00

exp a

B

Ek T T

t tæ ö

= ç ÷ç ÷-è ø(4)

and the best fits of the experimental data (the logarithmic variation of relaxation time”τ” as afunction of 1/(TF ‐ T0) as shown in Figure 8a yields the following parameters: interparticleinteraction strength T0 = 39.3 K and relaxation time constant τ 0 = 7.3 × 10−8 s for Co2SnO4. Here,we define the freezing temperature for each frequency is TF, angular frequency ω as 2π f (ω =1/τ), kB is the Boltzmann constant, and Ea is an activation energy parameter. Such large value ofτ0 indicates the presence of interacting magnetic spin clusters of significant sizes in thepolycrystalline Co2SnO4 system. The origin of such spin clusters may arise from a short‐rangemagnetic order occurring due to the competition between ferrimagnetism and magneticfrustration. Another characteristic feature that the spin‐glass systems follows is the power law(Eq. (5)) of critical slowing down in a spin‐glass phase transition at TSG (note that the TP(f) datarepresent a relatively small temperature interval):

0 1z

g

TT

u

t t-

æ ö= -ç ÷ç ÷

è ø(5)


85

Figure 7(a). The temperature dependence of the ac‐magnetic susceptibilities (i) real χ′(T) component and (ii) imaginaryχ″(T) component of bulk polycrystalline Co2SnO4 system recorded at various frequencies under warming condition us‐ing dynamic magnetic field of amplitude hac = 4 Oe and zero static magnetic field Hdc = 0. The lines connecting the datapoints are visual guides [27].

Figure 7(b). The temperature dependence of the ac‐magnetic susceptibilities (iii) real χ′(T) component and (iv) imagi‐nary χ″(T) component of bulk polycrystalline Co2TiO4 system recorded at various frequencies under warming condi‐tion using dynamic magnetic‐field of amplitude hac = 4 Oe and zero static magnetic field Hdc = 0. The lines connectingthe data points are visual guides [33].


The least‐square fit using the power law of the data shown in Figure 7 is depicted in Figure 8b.Here, TSG is the freezing temperature, τ0 is related to the relaxation of the individual clustermagnetic moment, and zν is a critical exponent. The least‐square fit analysis for Co2SnO4 givesTSG = 39.6 K, τ0 = 1.4 × 10−15 s, and zν = 6.4. Since the value of zν obtained in the present case lieswell within the range (6–8) of a typical spin‐glass systems; thus, one can conclude thatCo2SnO4 exhibits spin‐glass‐like phase transition across 39 K just below the TN ∼ 41 K [20, 27].In these studies, the difference in T0 and TSG is very small (∼0.3 K) suggesting the closeresemblance between the current Co2SnO4 system and the compounds exhibiting spin‐glass‐like transition. However, the situation for Co2TiO4 is bit different; in particular, the best fit tothe Vogel‐Fulcher law yields T0 = 45.8 K and τ0 = 3.2 × 10−16 s and the power law yielded fairlyunphysical values of the fitting parameters: for example, τ0 ~ 10−33 s with zν > 16, indicating thelack of spin‐glass‐like phase transition [33]. Although, the magnitude and shift of the ac‐susceptibility values both χ′(T) and χ″(T) strongly suppressed in the presence of dc‐magneticfield (HDC) in a similar way as it occurs in a typical spin‐glass system perfectly following thelinear behavior of H2/3 versus TP (AT‐line analysis). Under such tricky situation, it is verydifficult to conclude that Co2TiO4 is a perfect spin‐glass or not (of course one can call it as apseudo‐spin‐glass system). Nevertheless, the ac‐magnetic susceptibility data and its analysissuggested that the both Co2SnO4 and Co2TiO4 systems consist of interacting magnetic clustersclose to a spin‐glass state.

Another interesting feature of both Co2SnO4 and Co2TiO4 is that they show asymmetry in M‐H hysteresis loops unveiling giant coercivities and bipolar exchange bias under both ZFC andFC cases below their TN [27, 31, 33]. Earlier studies by Hubsch et al. have shown unusualtemperature dependence of coercive field HC(T) in polycrystalline Co2TiO4 sample where theM‐H loops were measured in 20‐kOe field at different temperatures below 60 K [31]. It is wellknown that the discovery of exchange‐bias (HEB) effect in the structurally single‐phasematerials with mixed magnetic phases has recently gained tremendous attention because ofits technological applications in the development of Read/Write heads of the magnetic

Figure 8. The best fit of the relaxation times to the (a) Vogel‐Fulcher law and the (b) power law for the spinels Co2SnO4

and Co2TiO4.


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recording devices [41]. Generally, HEB has been experimentally observed only in the systemscooled in the presence of external magnetic field (FC mode) from above the Néel temperatureor spin‐glass freezing point. Such systems usually comprise of variety of interfaces such asferromagnetic (FM)‐antiferromagnetic (AFM), FM‐SG, FM‐ferrimagnetic, AFM‐ferrimagnetic,and AFM‐SG [41–49]. However, few recent papers have reported significant HEB even underthe zero‐field‐cooled samples of bulk Ni‐Mn‐In alloys and in bulk Mn2PtGa [48, 49]. The sourceof such unusual HEB under zero‐field‐cooled sample was attributed to the presence of complexmagnetic interfaces such as ferrimagnetic/spin‐glass or AFM/spin‐glass phases [48–51]. Somerecent reports have suggested that large exchange anisotropy can originate from the exchangeinteraction between the compensated host and ferromagnetic clusters [48–51]. Strikingly,Hubsch et al. observed the HC→0 anomalies across TCMP, TSG, and TN in the temperature‐dependent data of HC for Co2TiO4 samples [31]. Slightly different results were reported byNayak et al. in Ref. [33], where HC values drops monotonically on approaching TN. However,the behavior of temperature dependence of exchange‐bias field HEB(T) and remanent magnet‐ization MR(T) in Ref. [33] closely resembles with the trend of HC(T) reported by Hubsch et. al.in polycrystalline Co2TiO4 samples. On the other hand, the temperature behavior of HEB(T),HC(T), and MR(T) in Co2SnO4 is way different from that of Co2TiO4 though they are isostructuralwith each other. It is likely that the different magnitudes and different temperature depend‐ences of the moments on the Co2+ ions on the “A”‐ and “B”‐sites in Co2SnO4 are responsible forthe anomalous behavior in the HEB(T), HC(T), and MR(T) observed below TN. Moreover, inCo2SnO4 below about 15 K, the data suggest that there is nearly complete effective balance ofthe antiferromagnetically coupled Co2+ moments at the”A”‐ and”B”‐sites leading to negligiblevalues of HC and MR.

Results from neutron diffraction in Co2TiO4 suggested the presence of canted‐spins, likelyresulting from magnetic frustration caused by the presence of nonmagnetic Ti4+ ions on the”B”‐sites. A similar canting of the spins might be present in Co2SnO4 although neutron diffractionstudies are needed to verify this suggestion [27, 31, 33]. Other Co‐based spinel compounds thatdisplay the reversal in the orientation of the magnetic moments along with negative magnet‐ization due to the magnetic‐compensation phenomena are CoCr2O4 and Co(Cr0.95Fe0.05)2O4 [3,52, 53].

4. Magnetic properties of bulk and nanocrystalline Co2MnO4

Among various Co2XO4 (X = Mn, Ni, Co, Zn, etc.) spinels, Co2MnO4 has retained a unique place.In particular, Mn‐ and Co‐based spinel oxides have gained considerable interest in the recentpast due to their numerous applications in the Li‐ion batteries [54, 55], sensors [56–58],thermistors [59], energy‐conversion devices [60], and as a catalyst for the reduction of nitrogenoxides [61]. Moreover, Co2MnO4 nanocrystals have demonstrated outstanding catalyticproperties for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) [60].ORR and OER are the essential reactions in the electrochemistry‐based energy‐storage andenergy‐conversion devices. Co2MnO4 has shown superior catalytic activities compared to thecommercial 30 wt% platinum supported on carbon black (Pt/C). Due to the special surface


morphology [62], Co2MnO4 spinel is a very promising pseudo‐capacitor material [63, 64].Co2MnO4 has also demonstrated potential applications for protective coating on ferritestainless steel interconnects in solid‐oxide fuel cells (SOFCs) [65, 66]. Furthermore, colossalmagnetoresistance (CMR) has been observed in the Mn‐ and Co‐based spinel oxides [67].

In addition to the novel catalytic properties, Co2MnO4 spinel exhibits intriguing magneticproperties. Lotgering first observed the existence of ferromagnetic ordering in Co2MnO4

spinels [68]. Ríos et al. systematically studied the effect of Mn concentration on the magneticproperties of Co3‐xMnxO4 solid solutions prepared by spray pyrolysis [69]. As we havediscussed in Section 2 that Co3O4 has an antiferromagnetic order with TN = 30 K. When wereplace Co in Co3O4 by Mn cation, large ferromagnetic ordering appears, which ultimatelydominates the antiferromagnetic ordering at x = 1. Therefore, pure Co2MnO4 shows ferromag‐netic behavior and this has been confirmed by detailed magnetic measurements [70, 71].However, for value of x other than 0 (Co3O4) and 1 (Co2MnO4), both ferromagnetic andantiferromagnetic magnetic exchange interactions coexist in the system, which yields aferrimagnetic ordering in the Co3‐xMnxO4 (0 < x < 1) solid solutions [72]. Tamura performedpressure‐dependent study of Curie temperature (TC) and found that TC decreases with increasein pressure [71].

Pure Co2MnO4 possess a cubic inverse‐spinel structure: (B3+)[A2+B3+]O4 (shown in Figure 9). Inan ideal case, the octahedral [B] sites are occupied by divalent cations together with half of thetrivalent cations and the rest of the trivalent cations occupy the tetrahedral (A) sites in thespinel structure. However, due to the presence of different oxidation states of Mn and Co cati‐ons at (A) and [B] sites, the actual cationic distribution of Co2MnO4 is very complex and it hasbeen a topic of considerable debate [59, 70–84]. Different sample preparation conditions alsoplay an important role in the cationic distribution of Co2MnO4. On the basis of X‐ray diffrac‐tion, electrical conductivity, magnetic, physiochemical, and neutron diffraction measure‐ments, several different cationic distributions for nonstoichiometric Co3‐xMnxO4 (0 < x < 1) havebeen reported in literature [59, 70–84]. From the magnetic measurements, Wickham and Croft

proposed the following cationic distribution: Co2 +[Co2 − �3 + Mn�3 +]O4(0 < � < 2) for solid solu‐

tions of Co3‐xMnxO4 systems obtained after the thermal decomposition of co‐precipitated man‐ganese and cobalt salts [72]. Later studies by Blasse suggested a different cationic distribution:Co2 +[Co2 − �2 + Mn�4 +]O4 [73]. Based on the physicochemical properties, Ríos et al. proposed a

more complicated cationic distribution: Co0.882 + Mn0.122 + [Co0.873 + Co0.222 + Mn0.093 + Mn0.764 + ■0.06]O4 for

Co2MnO4 powder samples prepared by thermal decomposition of nitrate salts [74]. From theneutron diffraction and magnetic measurements, Boucher et al. reported the cationic distribu‐

tion Co2 +[Co2 − �3 + Mn�3 +]O4 similar to the one reported by Wickham and Croft [72, 75]. Yama‐

moto et al. [76] performed neutron diffraction measurements on Co2MnO4 oxides prepared bychemical methods at low temperatures, and reported Mn1‐nCon[MnxCo2‐n]O4 as atomic distri‐bution. Here, n is the inversion parameter of the inverse‐spinel structure. Gautier et al. sug‐

gested two different possible cationic distributions: Co2+[Co3+Mn0.352 + Mn0.293 + Mn0.364 + ]O4 and


89

Co2+[��0.953 + Mn0.0152 + Mn0.503 + Mn0.4854 + ■0.05]O4 [77, 78]. On the contrary, the electrical conductivity

measurements suggest a different cationic distribution: Co2+[��2 +Co2(1 − �)3 + Mn�4 +]O4, andCo2+[Co2+Mn4+]O4 or Co3+[Co3+Mn2+]O4 [59, 79] for Co2MnO4 spinel. Aoki studied the phase

diagram and cationic distribution of various compositions of manganese and cobalt mixedspinel oxides [80]. He further investigated the effect of temperature and Mn concentration onthe structure of manganese‐cobalt spinel oxide systems. Control over morphology, crystallitesite, grain size, and specific surface area of Co2MnO4 powders can be achieved by thermaldecomposition of precursors in a controlled atmosphere [81, 82].

Figure 9. Cubic inverse‐spinel structure of Co2MnO4 in Fd‐3m (227) space group.

In 2008, Bazuev et al. investigated the effect of oxygen stoichiometry on the magnetic proper‐ties of Co2MnO4+δ [83]. Accordingly, two oxygen‐rich compositions, (i) Co2MnO4.62 and (ii)Co2MnO4.275, were prepared by the thermal decomposition of presynthesized Co and Mnbinary oxalates (Mn1/3Co2/3C2O4· 2H2O). Above studies also report existence of anomalousbehavior in the magnetic properties of Co2MnO4.275 spinel at low temperatures and highmagnetocrystalline anisotropy in Co2MnO4.62. Bazuev et al. also noticed that TN of Co2MnO4+δ

is highly sensitive to the oxygen stoichiometry, imperfections in the cationic sublattice andvariation in the Mn oxidation states. The imperfect Co2MnO4+δ inherits ferrimagnetic ordering

that arises due to the antiferromagnetic exchange between Co2+ (��4�2�3 ) and Mn4+ (�2�3 ��0))

cations located at the tetrahedral and octahedral sites, respectively. To further investigate theelectronic states of Mn and Co cations in the Co2MnO4 lattice, Bazuev at al. employed the X‐ray absorption near‐edge spectroscopy (XANES) to probe the electronic states of the absorbingatoms and their local neighborhood [83]. XANES spectra of both Co2MnO4.62 and Co2MnO4.275

compositions revealed that Co is present in both Co2+ and Co3+ oxidation states while Mn ispresent as Mn4+ and Mn3+. Additionally, it was found that Mn is located in a higher symmetryoctahedral crystal field environment [83]. Bazuev at al. further proposed following cationic


distributions for Co2MnO4.275 and Co2MnO4.62 compositions: Co0.9362 + [Co0.936III Mn0.4213 + Mn0.5154 + ]O4and Co0.662 + [Mn0.8664 + Co1.072III ]O4, respectively. Here, CoIII is a low‐spin cation while Co2+ and

Mn3+ are high‐spin cations.

Co2MnO4 spinels have gained peculiar interest of researchers due to their unusual magnetichysteresis behavior at low temperatures. Joy and Date [70] first observed the unusual magnetichysteresis behavior in Co2MnO4 nanoparticles below 120 K. By means of the magnetichysteresis loop measurements at low temperatures, they realized that the initial magnetizationcurve (virgin curve) lies outside the main hysteresis loop at 120 K. However, for T > 120 K, theyobserved normal hysteresis behavior in Co2MnO4. This unusual behavior of hysteresis loop atlow temperatures can be associated with the irreversible domain wall motion. At low magneticfields (H < HC), domain walls experience substantial resistance during their motion withincreasing magnetic field. Similar behavior has been observed for some other alloys [85–87].Such irreversible movement of domain walls was ascribed to the rearrangement of valenceelectrons at low temperatures. Generally, in a system with mixed oxidation states of Mn at hightemperatures, short‐range diffusion of Co ions, Co3+ ⇆ Co2+ associated with Mn3+ ⇆ Mn4+, getsactivated at low temperatures. This may cause change in the local ordering of the ions at theoctahedral sites. Consequently, the resistance for domain wall motion increases and this slowsdown the motion of domain walls. Soon after Joy and Date, Borges et al. [84] confirmed thatthe unusual hysteresis of Co2MnO4 compound indeed arises due to the irreversible domainwall motion. Borges et al. prepared various different size nanoparticles of Co2MnO4 by Pechinimethod and performed the magnetic hysteresis measurements at low temperatures [84]. Theyobserved that the samples below a critical diameter (d < 39 nm) exhibit normal hysteresisbehavior, while the bulk grain size samples (d ∼200 nm) show unusual hysteresis behavior atlow temperatures. Using the spherical particle model, Borges et al. further calculated thecritical diameter (dcr) of a single‐domain wall in Co2MnO4 and obtained that dcr = 39 nm [88].Therefore, all particles with diameter d< dcr can be considered as a single‐domain particle. Sinceparticles with d < dcr show normal hysteresis while particles with d > dcr show unusual hysteresisbehavior, one can conclude that the unusual hysteresis behavior is indeed due to the irrever‐sible motion of the domain walls.

The dynamic magnetic properties of Co2MnO4 nanoparticles of average diameter 28 nm werereported by Thota et al. [89]. A detailed study of dc‐ and ac‐magnetic susceptibility measure‐ments of these nanoparticles reveals the low temperature spin‐glass‐like characteristicstogether with the memory and aging effects (Figure 10). Figure 10 shows the temperaturedependence of real and imaginary part of the ac‐susceptibility (χ′(T) and χ″(T)) of Co2MnO4

nanoparticles recorded at different values of frequencies (f) between 1 Hz and 1.48 kHz at apeak‐to‐peak amplitude of 1 Oe. Both χ′(T) and χ″(T) exhibit a sharp peak at the onset offerromagnetic ordering (TC = T1 = 176.4 K) and a broad cusp centered at T2 (<TC).

The temperature at which both χ′(T) and χ″(T) attain the maximum value shifts toward high‐temperature side as the frequency increases from 1 Hz and 1.48 kHz similar to spin‐glassbehavior. Such frequency dependence of χ′(T) and χ″(T) follows the Vogel‐Fulcher law (Eq. (4)and insets of Figures 10a(ii) and b(ii)) and power law of critical slowing down (Eq. (5) and


91

insets of Figures 10a(i) and b(i)). Least‐square fit to these equation yields the followingparameters (insets of Figure 10): interparticle interaction strength ( T0) = 162 K for T1 (118 K forT2) and relaxation time constant τ0 = 6.18 × 10−15 s for T1 (4.4 × 10‐15 s for T2), critical exponent(zν) = 6.01 for T1 (7.14 for T2), and spin‐glass transition temperature (TSG) = 162.6 K for T1 (119.85K for T2). Since the values of zν for both the peaks T1 and T2 of Co2MnO4 nanoparticles lie wellwithin the range (6–8) of a typical spin‐glass systems, one can conclude that Co2MnO4 exhibitsspin‐glass‐like phase transition across 162.6 K just below the TC ∼ 176.4 K [89]. Figure 11ashows the magnetization relaxation of Co2MnO4 nanoparticles under ZFC and FC protocolswith a temperature quench to 70 K at H = 250 Oe [89]. The magnetization relaxation duringthe third cycle appears as a continuation of first cycle (Figures 11b and c). Relaxation of ZFCmagnetization with temperature quenching confirms the existence of memory effects inCo2MnO4 nanoparticles. A noticeable wait‐time (twt) dependence of magnetization relaxation(aging) at 50 K in both MZFC and MFC was noticed in these Co2MnO4 nanoparticles, which furthersupports the presence of the spin‐glass behavior observed in this system.

Figure 10. The real and imaginary components of the ac‐magnetic susceptibilities (χ′(T) and χ″(T)) of Co2MnO4 nano‐particles measured at various frequencies. The insets a(i) and b(i) represent the Vogel‐Fulcher law whereas the insetsa(ii) and b(ii) represent the power law of critical slowing down for both the peaks T1 and T2.


Figure 11. Magnetization relaxation M(t) under ZFC and FC protocols with a temperature quench to 70 K at H = 250Oe. The continuation of the first and third relaxation process during (b) ZFC and (c) FC cycles.

The high‐temperature inverse magnetic susceptibility (1/χZFC versus T) data of Co2MnO4

nanoparticles (Figure 12) fit well with the Néel's expression for ferrimagnets:

0

0

1 1TC T

sc c q

é ù= + - ê ú-ë û(6)

Figure 12. The scattered data represent the high‐temperature inverse magnetic susceptibility (1/χZFC versus T) ofCo2MnO4 nanoparticles and the solid line represents the best fit to the Néel's expression for ferrimagnets Eq (6).


93

The fit (red line in Figure 12) yields: C = 0.0349 emu K/g Oe, �0 = 4.5 × 10‐5 emu/g Oe, �0 = 5.76× 104 g Oe K/emu, � = 169.8 K, and the asymptotic Curie temperature Ta = C/�0 = 775.6 K [90,91]. Ta gives us information about the strength of antiferromagnetic exchange couplingbetween Mn3+ and Mn4+ at octahedral sites. Moreover, the effective magnetic moment μeff

calculated using expression: � = ��eff23�B turnouts to be 8.13 μB.

5. Concluding remarks

In this review, magnetic properties of bulk and nanoparticles of the Co‐based spinels Co3O4,Co2SnO4, Co2TiO4, and Co2MnO4 have been summarized. The fact that the observed magneticproperties of these spinels are so different is shown to result from the different occupation ofthe cations on the A‐ and B‐sites and their different electronic states at these sites. The richnessof the properties of spinels thus results from these differences.

Acknowledgements

The authors thank Prof. M. S. Seehra for his suggestions and guidance in organizing thischapter. Sobhit Singh acknowledges the support from the West Virginia University Librariesunder OAAF program.

Author details

Subhash Thota1* and Sobhit Singh2

*Address all correspondence to: [email protected]

1 Department of Physics, Indian Institute of Technology, Assam, India

2 Department of Physics & Astronomy, West Virginia University, Morgantown, USA

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nature of magnetic ordering in cobalt based spinels

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